Definitions
Whether you are a first-time buyer is a stricter test than it sounds.
For tax purposes, a first-time buyer is someone who has never owned a freehold or leasehold interest in a dwelling — anywhere in the world, at any time, by any route. That includes a share inherited from a relative, a property owned jointly with a former partner, and a home owned abroad before you moved to the UK.
It also applies to everyone on the purchase. If you buy jointly and one of you has owned before, the purchase is not a first-time buyer purchase, and the relief that applies to the tax on it is lost for the whole transaction rather than for half of it.
Lenders use their own, looser definition for product eligibility — usually meaning you do not currently own a property — so it is entirely possible to qualify for a first-time buyer mortgage product and not qualify for the tax relief. They are separate questions and are worth asking separately.
→Property tax on a purchase is devolved: England and Northern Ireland, Scotland and Wales each run a different regime, with different thresholds and different relief.
→The tax is payable from your own funds on completion. It cannot be added to the mortgage, so it has to be saved for alongside the deposit.